Stabilization of polytopic delay difference inclusions : time-varying control Lyapunov functions

R.H. Gielen, M. Lazar

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review


This paper deals with stabilization of polytopic delay difference inclusions (DDIs) via the Razumikhin approach. As not every DDI that is globally exponentially stable (GES) admits a standard Lyapunov-Razumikhin function (LRF), timevarying Lyapunov functions are proposed as a tool for stability analysis and stabilizing controller synthesis for polytopic DDIs. It is shown that any polytopic DDI that is GES admits a quadratic time-varying Lyapunov-Krasovskii function and, under an additional mild assumption, it also admits a quadratic time-varying LRF. These results are further exploited to derive a stabilizing receding horizon control scheme that does not suffer from an exponential increase in complexity when the size of the delay increases. The proposed control scheme requires solving on-line a low-dimensional semi-definite program.
Original languageEnglish
Title of host publicationProceedings of the 49th IEEE Conference on Decision and Control, December 15-17, 2010, Atlanta, Georgia
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
ISBN (Print)978-1-4244-7745-6
Publication statusPublished - 2010


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